Q. 24.0( 4 Votes )
Differentiate log(1 + x2) with respect to tan–1x.
Answer :
Let u = log(1 + x2) and v = tan–1x.
We need to differentiate u with respect to v that is find
.
On differentiating u with respect to x, we get
We know
[using chain rule]
However, 
and derivative of a constant is 0.
Now, on differentiating v with respect to x, we get
We know 
We have 
Thus, 
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